Police who chased a man before he jumped into Parramatta River and drowned say he may have been linked to a suspicious luxury car found minutes earlier.

Officers on patrol located an abandoned white BMW about 3.45am (AEDT) on Thursday in Nordica St, Ermington, in Sydney's west.

Their suspicions about the vehicle led them to pull over a taxi about 30 minutes later in the same street.

Police approached the cab and began making inquiries when a woman and a 31-year-old man ran from the vehicle.

"Police clearly had suspicions as to the occupants of that cab (and) whether (they were) related to the BMW that had been found abandoned," Acting Assistant Commissioner Dave Eardley told reporters in Sydney.

The woman was stopped a short distance later, but the man led officers on a foot pursuit for about 50 to 100 metres to the edge of Parramatta River.

It was very dark and by the time they reached the river's edge, they had lost sight of him.

They searched the embankment and alerted the Dog Squad and Water Police to assist in the search.

The man's body was found in the river about 1.5km east of where he was believed to have entered the waterway.

"Anytime you have someone who loses their life through something so meaningless is always a tragedy," Mr Eardley said.

Police have formed a critical incident investigation into the man's death.

No shots were fired and police would not comment on what raised their suspicions about the BMW.

A number of items were seized from the scene, including a handbag and jewellery, but police would not comment if robbery was a factor.

The man and woman's relationship was unknown, police said, and they are working to determine if alcohol or drugs were a factor.

It was not known if the taxi driver somehow signalled police before they pulled him over, but detectives expect to interview him.